Question: Solve for $x$, $ -\dfrac{6}{5x^2} = -\dfrac{3}{25x^2} - \dfrac{x + 10}{5x^2} $
Solution: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $5x^2$ $25x^2$ and $5x^2$ The common denominator is $25x^2$ To get $25x^2$ in the denominator of the first term, multiply it by $\frac{5}{5}$ $ -\dfrac{6}{5x^2} \times \dfrac{5}{5} = -\dfrac{30}{25x^2} $ The denominator of the second term is already $25x^2$ , so we don't need to change it. To get $25x^2$ in the denominator of the third term, multiply it by $\frac{5}{5}$ $ -\dfrac{x + 10}{5x^2} \times \dfrac{5}{5} = -\dfrac{5x + 50}{25x^2} $ This give us: $ -\dfrac{30}{25x^2} = -\dfrac{3}{25x^2} - \dfrac{5x + 50}{25x^2} $ If we multiply both sides of the equation by $25x^2$ , we get: $ -30 = -3 - 5x - 50$ $ -30 = -5x - 53$ $ 23 = -5x $ $ x = -\dfrac{23}{5}$